Abuse of statistics – transitive property

December 8, 2008

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This will likely become a mini-series … statistics are great, but can be abused.

Today’s focus is on the “transitive” property of statistics. My example will be an issue that many people are well aware of. The issue is important and is a problematic societal issue. I am definitely not suggesting that the problem doesn’t exist – but I am suggesting that the arguments have at times been twisted to say things that the number don’t necessarily support.

Fact 1: Members of group A are paid less than members Group B for the same work
Fact 2: Members of group A, on average, have salaries that are 50% of those of members of group B

thus, the creation of
“fact” 3
Members of group A on average make, on average, 50% of members of group B, for the same work.

The only problem with this is that this is overly simplistic. You cannot blend the first two facts. Too many other variables exist.

Let’s illustrate:

Group A, 100 people
6 brain surgeons @ 135,000 = 810,000
94 engineers @ 45,000 = 4,230,000
Total = 5,040,000

Group B, 100 people
50 brain surgeons @ 150,000 = 7,500,000
50 engineers @ 50,000 = 2,500,000
Total = 10M

Let’s test facts 1 and 2

Fact 1: Are members of group A paid less than members of group B for the same work? Yes. They make 10% less.
Fact 2: Are members of group A, on average, paid ~50% of the salary of members of group B? Yes. 50.4%

But when we come to “fact” 3:
Members of group A on average make, on average, 50% of members of group B, for the same work.

This is not true. Members of group A make 90% of what members of group B make for the same work.

Keep an eye open and you’ll see occasional use of the “transitive” property by otherwise reputable sources. Why? Either because the person doesn’t know any better, or because it’s easier than delving deeper to find the “split” statistics – and 90% of people aren’t going to see the problem. The key point here – when you read the news, you should not only scrutinize the facts for accuracy, but also the logic used to piece the story together. The best statistics in the world cannot undo the harm of illogical thinking.

End note: With this particular example, there is the issue of why members of group A tend to have less than members of group B. Is this due to personal preference, lifestyle choices, or a lack of opportunity. This is a good topic for discussion, but it is beyond the point of this article – that people need to analyze the statistics more closely.

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